This might be because Word overrides system shortcuts (i.e. the 'paste without formatting' in this case). Google Docs tries to do this in the browser as well, but it happens to support this particular shortcut.
Is "paste without formatting" really a system shortcut? I'd never heard of it before. I feel like it might be something semi-standard that apps implement?
I believe I may have seen it in a shortcut editor somewhere, but I suppose I could be misremembering or that could have been a one-off implementation.